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Wilkins, who was reported to be "devastated" by Chelsea's decision not to renew his contract, left the club on Thursday after being notified of his departure.
Ancelotti -- who said in a recent autobiography that Wilkins was instrumental in helping the Italian lead Chelsea to the double last season -- said the 54-year-old had done a "fantastic job."
"I just want to say one thing," Ancelotti said Friday. "Ray was a fantastic assistant coach and I want to say thanks to him because he was a fantastic support last season and this.
"He did a fantastic job. He helped me and the team win the double. So the first thing is to say a lot of thanks to him.
"He is my friend. I have a fantastic relationship with him, and I will have a fantastic relationship with him. The club made this decision.
"It was a difficult decision for everyone, but I have respect for this decision. I have trust in all the staff who are working with me, but we have to move on now."
He added: "We have to look forward and focus on the next game. It will be an important season for us, and it's important to move on."
Chelsea are now mulling their options as they decide how to replace Wilkins, although first-team coach Paul Clement is now tipped to step up to assistant manager.